A necessary and sufficient condition for SDL constructions of optical FIFO queues

Recently, constructing optical queues by using optical crossbar Switches and fiber Delay Lines (SDL) has been recognized as a key research issue for all-optical packet switching. In this paper, we focus on SDL constructions of optical FIFO queues. We consider a network element consisting of a 1 × 2 optical crossbar switch, 2k + 1 2 × 2 optical crossbar switches, and 2k + 1 fiber delay lines of lengths ℓ₀, ℓ₁, ..., ℓ_2k. The main contribution of this paper is to provide an explicit control scheme that explicitly specifies the connection patterns of the optical crossbar switches, and obtain a necessary and sufficient condition on the lengths ℓ₀, ℓ₁, ..., ℓ_2k (specifically, the condition in (A1) in Section I) for such a network element to be operated as an optical FIFO queue with buffer equation under our proposed control scheme. The key idea in our proposed control scheme is to operate the network element such that packets stored in the network element satisfy an ordered property and a circularly contiguous property, which lead to the properties required of a FIFO queue.